Numerical Investigation Of Mode Transition Mechanisms In Radio Frequency Inductively Coupled Plasma

Radio frequency inductively coupled plasma (rf-ICP) is one of the promising plasma sources in the fields of semiconductor fabrication and material science etc, due to their advantages e.g. high plasma density at low pressures, reduced dielectric damage, independently controllable ion energy and low price and so on. It is well known that ICP involves two plasma modes, electrostatic (E) and electromagnetic (H), arising from the special excitation of the discharge. When adjusting the power of rf source, the plasma sustaining mechanism can be varied between E and H modes, accompanied by the sudden variations of the plasma parameters, e.g. electron density and temterature, etc, and electrical parameters in the circuit elements, e.g. coil current and voltage drop, etc. The mode transition and the evolution behavior of plasma condition can significantly affect the plasma-assisted etching and deposition processes. Therefore, it is necessary to investigate the mode transition, and the simulated results can be useful for technically controlling and optimizing the plasma processing technology in micro-and nano-meter scales.To this end, both the fluid model and Monte Carlo/fluid model with nonlinear coupling of multi physical fields are established on a planar coil ICP reactor and used to simulate the evolution of plasma dynamics during mode transition in argon ICP source. The mechanisms behind the mode transition and hysteresis are also analyzed.In Chapter 2, the expressions of the rf electric and magnetic fields in the chamber volume, when E and H modes coexist, were deduced based on Maxwell equations. Then the profiles of rf fields are coupled with two-dimensional fluid model, based on local approximation of density. The combined model is used to simulate the behavior of mode transition by adjusting the coil current. The evolutions of electron density and temperature during the transition are investigated, especially for their sudden variations at the mode transition point. The results show that the discharge transfers from E mode dominated to H mode dominated, when increasing the coil current. At the certain value of current, the density and power increase suddenly. In addition, the spatial distributions of plasma density, temperature and rf fields at different coil currents, and their evolutions during the mode transition, are systematically examined. Moreover, the variations of the inductive and capacitive components of absorbed power, with the coil current, are also observed. In Chapter 3, a hybrid Monte Carlo/fluid model was developed to investigate the effect of nonlocal characteristic of electrons at low pressures on mode transition. Among the hybrid model, the macro behavior of plasma condition, e.g. diffusion and flow, is determined by the fluid module, while the details of collisions between electrons and neutral particles, rate coefficients, EEDF and electron dynamic temperature are all computed by the electron Monte Carol (MC) part. The simulations show that after the nonlocal behavior of electrons being considered, the mode transition at different pressures evolves distinctly when increasing the coil current. When the pressure is low (20 mTorr), the transition seems more continuous. Increasing the pressure to 50 mTorr, the mode transition occurs more abruptly. When the pressure is increased further, there is still remarkable region in the axis of coil current where mode transition is occurred, but the range of coil current is wider. In addition, the evolutions of the characteristic distributions of plasma density, temperature and potential with mode transition are observed at different pressures. The difference of the profiles caused by the pressure is interpreted in terms of the different heating mechanisms of stochastic and Ohm.The EEDFs of E and H modes at different pressures are explored. The EEDFs of two modes significantly differ, due to the diverse structures of inductive and capacitive rf fields, and the distinct energy loss mechanisms. Moreover, the evolution of EEDFs with mode transition also depends on the pressure. When pressure is low, a striking peak is observed at a low energy during the EEDF profile of E mode, presumably owning to the electrons trapped by the ambipolar potential well. This low-energy peak may still be intensified by the Ramsauer effect. When the pressure is increased, the situation seems opposite. During H mode, the high-energy electrons are depleted severely and meanwhile the ratio of low energy electrons in H mode is more than the case in E mode. We attribute this to the fact that high density and strong emission are produced in the H mode, and the inelastic collisions may lead to huge consumption of the high energy electrons. The simulated trends of EEDF with mode transition agree with experiment qualitatively.The EEPFs are also studied in the same way. At low pressure, EEPF evolves from bi-Maxwellian to Maxwellian type during the elastic energy range, as the mode transfers. In addition, due to the inelastic collision, flexion appears at about the excitation threshold in the EEPFs of two modes. Through the comparison of EEPF evolution at high pressure between the model and the experiment, we deduce that it is due to the e-e Coulomb collision that EEPF evolves from Druyvesteyn to Maxwellian distribution during the transition.In Chapter 4, the effects of metastable atoms and multistep ionization on mode transition are investigated using the hybrid model, and meanwhile the evolution of metastables during mode transition is examined. (1) When metastable atoms are included, the shape of dependence of the electron density on power is almost unchanged; however the magnitude is magnified as a whole due to multistep ionization. The electron temperature decreases monotonically as the deposited power increases, the decrease being particularly marked in the H mode. (2) The density of metastable atoms as a function of power deposited increases during the E mode, reaches a maximum close to the point of transition to H mode and then drops during H mode. The distribution of metastables is localized under dielectric window when discharge transfers to H mode. (3) The EEDF profiles in the E mode are influenced only slightly by the presence of metastables due to the relatively low metastable density at low coil current. However, in H mode, due to the multistep ionization, the EEDF profile in the bulk plasma peaks at a lower energy.The spatial distributions of EEDFs in E and H modes are calculated throughout the plasma volume and the difference between the EEDF profiles is interpreted in terms of the plasma dynamics, the distribution characteristics of rf fields and the chamber structure etc. The presence of metastable atoms seems not change the overall characteristic of the distribution of EEDFs, implying that multistep ionization may not be the determined factor for the hysteresis. Moreover, a linearly increasing slope of plasma density with the deposited power is observed and no evidence of nonlinear mechanisms is detected.